Mathematics of a price war

In my last post I looked at two companies competing over a natural monopoly. We saw that once they started competing it would not then make sense for either company to drop out. This is why price wars tend to continue once they have started.

Here is the maths behind the problem:

To keep things simple let’s assume that the two companies are only going to compete for two years.

They can drop out before they even enter the market, after a year or after two years.